MHT CET 2019 Math Solved Paper

Equation of family of circles whose radius is 4 is :
(x−a)2+(y−b)2=16......(i)
(where a & b are arbitrary constant)
Differentiating we get:
2(x−a)+1(y−b)y1 .......(ii)
(y1=

dy

dx

)
Again differentiating we get:
1+y1.y1+(y−b)y2=0 ‌‌‌(y2=

d2y

dx2

)
⇒(y−b)y2+(y−b)y2=0
(y−b)y2=−(1+y12)
⇒y−b=

(1+y12)

y2

......(iii)
from (ii) we get :
x−a=−(y−b)y1
∴ from (i) , we get :
(y−b)2y12+(y−b)2=16
⇒(y−b)2−(1+y12)=16
⇒(

(1+y12)2

y22

)(1+y12)=16 (from (iii))
⇒(1+y12)3=16y22
⇒[1+(

dy

dx

)2]3=16[

d2y

dx2

]2
∴ Order= 2 & degree = 2